The father is the absolute owner of his share in the property if the registered title deed mentions both the father and mother as buyers purchasing the property jointly.
If the above is yes, then the father can legally transfer his share in the porperty in favor of his second wife or to anyone of his choice by executing a registered gift deed.
His son cannot object to this nor can he claim a right over his father's share in the property for any reason, it is not maintainable in law and his case, if any in this regard, is tenable in law.
There is no question of first owner or second owner, both are joint owners.
Thus, as far as the share of the wife in this property, if the son claims ownership on the basis of the Will, then he has to prove that the will is valid by obtaining probate or letter of administration from a court of law, otherwise it can be said that his mother died intestate thereby the father is also having a share in his deceased wife's share of property. It means the son cannot claim his mother's entire share of property.
If you are for the society, you may better take a legal opinion from a local lawyer on such further issues before taking any wrong decision and run behind courts over the disputes or litigation.